document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=941784>Question 941784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> THE SUM OF AN INFINITE GEOMETRIC PROGRESSION IS 15 AND THE SUM OF THE SQUARES OF THESE TERMS IS 45. FIND THE SERIES.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #574132 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=574132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for sum of infinite GP is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"+a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2F%281-r%29+=15 ALIGN=MIDDLE  ALT=\"+a%2F%281-r%29+=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq(1)<BR>\n" );
document.write( "   <BR>\n" );
document.write( "HE SUM OF THE SQUARES OF THESE TERMS IS 45<BR>\n" );
document.write( "  hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2%2F%281-r%5E2%29+=45 ALIGN=MIDDLE  ALT=\"+a%5E2%2F%281-r%5E2%29+=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......eq(2)<BR>\n" );
document.write( "  divide eq(1) with eq (2)<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+a%2F%281-r%29%29%2F%28%28a%5E2%2F%281-r%5E2%29%29%29+=15%2F45 ALIGN=MIDDLE  ALT=\"+%28+a%2F%281-r%29%29%2F%28%28a%5E2%2F%281-r%5E2%29%29%29+=15%2F45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+a%2F%281-r%29%29%2F%28%28a%5E2%2F%281-r%29%281%2Br%29%29%29%29+=15%2F45 ALIGN=MIDDLE  ALT=\"+%28+a%2F%281-r%29%29%2F%28%28a%5E2%2F%281-r%29%281%2Br%29%29%29%29+=15%2F45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F1%29%2F%28a%2F%281%2Br%29+%29=1%2F3 ALIGN=MIDDLE  ALT=\"%281%2F1%29%2F%28a%2F%281%2Br%29+%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Br%29%2Fa=1%2F3 ALIGN=MIDDLE  ALT=\"%281%2Br%29%2Fa=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281%2Br%29+=3 ALIGN=MIDDLE  ALT=\"a%2F%281%2Br%29+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    move (1+r) to the right<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a=+%281%2Br%29%2A3 ALIGN=MIDDLE  ALT=\"+a=+%281%2Br%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " but from eq(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2F%281-r%29+=15 ALIGN=MIDDLE  ALT=\"+a%2F%281-r%29+=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "             move (1-r) to the right<BR>\n" );
document.write( "           <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a=+%281-r%29%2A15 ALIGN=MIDDLE  ALT=\"+a=+%281-r%29%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "            from above expressions<BR>\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Br%29%2A3++=+%281-r%29%2A15 ALIGN=MIDDLE  ALT=\"%281%2Br%29%2A3++=+%281-r%29%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         3+3*r= 15*1-r*15<BR>\n" );
document.write( "       3+3r =15-15r<BR>\n" );
document.write( "        move -15r to the left<BR>\n" );
document.write( "      3+3r+15r =15<BR>\n" );
document.write( "       3+18r =15<BR>\n" );
document.write( "         18r =15-3<BR>\n" );
document.write( "      18r =12<BR>\n" );
document.write( "         r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%2F18 ALIGN=MIDDLE  ALT=\"+12%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "           r= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   but a  = (1+r)*3<BR>\n" );
document.write( "           = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B%282%2F3%29%29%2A3 ALIGN=MIDDLE  ALT=\"%281%2B%282%2F3%29%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%2F3%29+%2B%282%2F3%29%29%2A3 ALIGN=MIDDLE  ALT=\"%28%283%2F3%29+%2B%282%2F3%29%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%283%2B2%29%2F3+%29%2A3 ALIGN=MIDDLE  ALT=\"+%28%283%2B2%29%2F3+%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = 5<BR>\n" );
document.write( "a= 5, r= 2/3<BR>\n" );
document.write( "series  =  5, 10/3, 20/9,...<BR>\n" );
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